Computes the log transformation with an offset,
including its inverse and the first two derivatives.
Usage
logofflink(theta, offset = 0, inverse = FALSE, deriv = 0,
short = TRUE, tag = FALSE)
log1plink(theta, offset = 0, inverse = FALSE, deriv = 0,
short = TRUE, tag = FALSE)
Value
For deriv = 0, the log of theta+offset,
i.e.,
log(theta+offset) when inverse = FALSE,
and if inverse = TRUE then
exp(theta)-offset.
For deriv = 1, then the function returns
d
theta / d
eta as
a function of theta
if inverse = FALSE,
else if inverse = TRUE then it returns
the reciprocal.
Here, all logarithms are natural logarithms,
i.e., to base e.
Arguments
theta
Numeric or character.
See below for further details.
offset
Offset value.
See Links.
For log1plink this argument should
not be used because the offset is
implicitly unity .
inverse, deriv, short, tag
Details at Links.
Author
Thomas W. Yee
Details
The log-offset link function is very commonly used
for parameters that
are greater than a certain value.
In particular, it is defined by
log(theta + offset) where
offset is the offset value. For example,
if offset = 0.5 then the value
of theta is restricted
to be greater than \(-0.5\).
Numerical values of theta close
to -offset or out of range
result in
Inf, -Inf, NA or NaN.
The offset is implicitly 1 in log1plink.
It is equivalent to logofflink(offset = 1)
but is more accurate if abs(theta) is tiny.
It may be used for lrho in
extbetabinomial provided
an offset log(size - 1)
for \(\eta_2\)
is included.
References
McCullagh, P. and Nelder, J. A. (1989).
Generalized Linear Models, 2nd ed.
London: Chapman & Hall.